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The number of integer points close to a polynomial. (English) Zbl 1424.11105

Summary: Let \(f(x)\) be a polynomial of degree \(n\geq 1\) with real coeffcients and let \(X\geq 2\) and \(\delta\geq 0\) be real numbers. Let \(\vert \vert .\vert \vert \) be the distance to the nearest integer. We obtain upper bounds for the number of solutions to the inequality \(\vert \vert f(x)\vert \vert \leq \delta\) with \(x\in[X,2X]\cap \mathbb{N}\).

MSC:

11J54 Small fractional parts of polynomials and generalizations
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